np (version 0.40-13)

npcmstest: Kernel Consistent Model Specification Test with Mixed Data Types

Description

npcmstest implements a consistent test for correct specification of parametric regression models (linear or nonlinear) as described in Hsiao, Li, and Racine (2007).

Usage

npcmstest(formula,
          data = NULL,
          subset,
          xdat,
          ydat,
          model = stop(paste(sQuote("model")," has not been provided")),
          distribution = c("bootstrap", "asymptotic"),
          boot.method = c("iid","wild","wild-rademacher"),
          boot.num = 399,
          pivot = TRUE,
          density.weighted = TRUE,
          random.seed = 42,
          ...)

Arguments

formula

a symbolic description of variables on which the test is to be performed. The details of constructing a formula are described below.

data

an optional data frame, list or environment (or object coercible to a data frame by as.data.frame) containing the variables in the model. If not found in data, the variables are taken from

subset

an optional vector specifying a subset of observations to be used.

model

a model object obtained from a call to lm (or glm). Important: the call to either glm or

xdat

a $p$-variate data frame of explanatory data (training data) used to calculate the regression estimators.

ydat

a one (1) dimensional numeric or integer vector of dependent data, each element $i$ corresponding to each observation (row) $i$ of xdat.

distribution

a character string used to specify the method of estimating the distribution of the statistic to be calculated. bootstrap will conduct bootstrapping. asymptotic will use the normal distribution. Defaults to boot

boot.method

a character string used to specify the bootstrap method. iid will generate independent identically distributed draws. wild will use a wild bootstrap. wild-rademacher will use a wild bootstrap with Rademac

boot.num

an integer value specifying the number of bootstrap replications to use. Defaults to 399.

pivot

a logical value specifying whether the statistic should be normalised such that it approaches $N(0,1)$ in distribution. Defaults to TRUE.

density.weighted

a logical value specifying whether the statistic should be weighted by the density of xdat. Defaults to TRUE.

random.seed

an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42.

...

additional arguments supplied to control bandwidth selection on the residuals. One can specify the bandwidth type, kernel types, and so on. To do this, you may specify any of bwscaling, bwtype, ckertype,

Value

• npcmstest returns an object of type cmstest with the following components, components will contain information related to Jn or In depending on the value of pivot:
• Jn
  the statistic Jn
• In
  the statistic In
• Omega.hat
  as described in Hsiao, C. and Q. Li and J.S. Racine.
• q.*
  the various quantiles of the statistic Jn (or In if pivot=FALSE) are in components q.90, q.95, q.99 (one-sided 1%, 5%, 10% critical values)
• P
  the P-value of the statistic
• Jn.bootstrap
  if pivot=TRUE contains the bootstrap replications of Jn
• In.bootstrap
  if pivot=FALSE contains the bootstrap replications of In
• summary supports object of type cmstest.

Usage Issues

npcmstest supports regression objects generated by lm and uses features specific to objects of type lm hence if you attempt to pass objects of a different type the function cannot be expected to work. If you are using data of mixed types, then it is advisable to use the data.frame function to construct your input data and not cbind, since cbind will typically not work as intended on mixed data types and will coerce the data to the same type.

References

Aitchison, J. and C.G.G. Aitken (1976), Multivariate binary discrimination by the kernel method, Biometrika, 63, 413-420.

Hsiao, C. and Q. Li and J.S. Racine (2007), A consistent model specification test with mixed categorical and continuous data, Journal of Econometrics, 140, 802-826.

Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.

Maasoumi, E. and J.S. Racine and T. Stengos (2007), Growth and convergence: a profile of distribution dynamics and mobility, Journal of Econometrics, 136, 483-508.

Murphy, K. M. and F. Welch (1990), Empirical age-earnings profiles, Journal of Labor Economics, 8, 202-229.

Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.

Wang, M.C. and J. van Ryzin (1981), A class of smooth estimators for discrete distributions, Biometrika, 68, 301-309.

Examples

# EXAMPLE 1: For this example, we conduct a consistent model
# specification test for a parametric wage regression model that is
# quadratic in age. The work of Murphy and Welch (1990) would suggest
# that this parametric regression model is misspecified.

data("cps71")
attach(cps71)

model <- lm(logwage~age+I(age^2), x=TRUE, y=TRUE)

plot(age, logwage)
lines(age, fitted(model))

# Note - this may take a few minutes depending on the speed of your
# computer...

npcmstest(model = model, xdat = age, ydat = logwage)

# Sleep for 5 seconds so that we can examine the output...

Sys.sleep(5)

# Next try Murphy & Welch's (1990) suggested quintic specification.

model <- lm(logwage~age+I(age^2)+I(age^3)+I(age^4)+I(age^5), x=TRUE, y=TRUE)

plot(age, logwage)
lines(age, fitted(model))

X <- data.frame(age)

# Note - this may take a few minutes depending on the speed of your
# computer...

npcmstest(model = model, xdat = age, ydat = logwage)

# Sleep for 5 seconds so that we can examine the output...

Sys.sleep(5)

# Note - you can pass in multiple arguments to this function. For
# instance, to use local linear rather than local constant regression, 
# you would use npcmstest(model, X, regtype="ll"), while you could also
# change the kernel type (default is second order Gaussian), numerical
# search tolerance, or feed in your own vector of bandwidths and so
# forth.

detach(cps71)

# EXAMPLE 2: For this example, we replicate the application in Maasoumi,
# Racine, and Stengos (2007) (see oecdpanel for details). We
# estimate a parametric model that is used in the literature, then
# subject it to the model specification test.

data("oecdpanel")
attach(oecdpanel)

model <- lm(growth ~ oecd +
            factor(year) +
            initgdp +
            I(initgdp^2) +
            I(initgdp^3) +
            I(initgdp^4) +
            popgro +
            inv +
            humancap +
            I(humancap^2) +
            I(humancap^3) - 1, 
            x=TRUE, 
            y=TRUE)

X <- data.frame(factor(oecd), factor(year), initgdp, popgro, inv, humancap)

npcmstest(model = model, xdat = X, ydat = growth)

detach(oecdpanel)